I just took a look on some of my long-running correspondence tournaments. In 2 of them the last pending games were “Paused”.
One of these games is on pause for 4 months, no stone played jet and the player which paused it isn’t around for month.
I asked the players in question to continue their games and will inform the tournament director if they don’t. But I wonder how many tournament games are unnoticed on pause.

I would like if the “Pause” is either not possible in correspondence tournaments or at least has some time limit.

Totally agree. Totally dude.
Scenario:
In a tournament Person A pauses his game with Person B.
Person B doesn’t mind or doesn’t care or has actually quit playing. (edit: or doesn’t notice.)
Whole tournament ends up paused indefinitely without the permission of person C,D,E etc. until someone realises what’s happened and involves a Mod.
It’s perfectly reasonable to pause a game by mutual consent but in a tournament no consent is sought or given by all the other participants.

In my experience, the directors do have that power. It might be, though, that instead of just calling the game result they have to actually disqualify one or both players from the tournament and then the game is ended by “Disqualification”.

Some people also play during the pause. To reduce notification spam? ^^ As long as they’re not the only people left playing, I don’t really mind. One of my opponents vanished for a month so I paused the game for 2 weeks, but he didn’t come back so I unpaused again…

Yea I wouldn’t disable it for tourneys in general (only for titled tourneys) but make it optional.